Learning Outcomes

Compare and contrast different methods for modeling implied volatility surfaces including stochastic volatility, local volatility, and jumps

Derive the characteristic function of log stock prices in settings with stochastic volatility and jumps; discuss and implement the pricing of European put and call options by Fourier inversion techniques

Implement an implied binomial tree and explain the formula for local volatility

Design efficient simulation schemes for pricing options with path-dependent payoffs and early exercise features

Implement simple finite difference schemes

Explain the decomposition of structured products into their underlying option components; understand the model risk associated with pricing and hedging exotic derivatives and structured products